Supersymmetric Hypermatrix Lie Algebra and Hypermatrix Groups Generated by the Dihedral Set $D_3$
Bibliographic record
Abstract
This work is an investigation into the structure and properties of supersymmetric hypermatrix Lie algebra generated by elements of the dihedral group $D_3$. It is based on previous work on the subject of supersymmetric Lie algebra (Schreiber, 2012).In preview work I used several new algebraic tools; namely cubic hypermatrices (including special arrangements of such hypermatrices) and I obtained an algebraic structure associated with the basis of the Lie algebra $sl_2$, and I showed that the basis elements $sl_2$ are generators of infinite periodic hypermatrix Lie algebraic structures with semisimple sub-algebras. The generated algebra has been shown to be an extended Lie hypermatrix algebra that has a classical Lie algebra decomposition composed of hypermatrices with periodic properties. The generators of higher dimensional Lie algebra were shown to be special supersymmetric, anti-symmetric and certain skew-symmetric hypermatrices. The present work takes a different look at the structure of periodic hypermatrix Lie algebra by using elements generating the classical dihedral group $D_3$. Using cubic dihedral symmetric hypermatrices (type: even-even, odd-odd, even-odd odd-even permutation) to generate Lie hypermatrix algebra I show that the extended dihedral algebra is a Lie hypermatrix algebras with special hypermatrix group properties, semisimple, symmetric, skew-symmetric, anti-symmetric, and anti-clockwise symmetric properties.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".